Quantum Information Processing, Vol. 6, No. 3, June 2007 (© 2007)
A Characterization of Global Entanglement
Peter J. Love,
Alec Maassen van den Brink,
M. H. S. Amin,
and A. M. Zagoskin
Received January 25, 2007; accepted February 13, 2007; Published online: May 15, 2007
We deﬁne a set of 2
− 1 entanglement monotones for n qubits and give a
single measure of entanglement in terms of these. This measure is zero except
on globally entangled (fully inseparable) states. This measure is compared to
the Meyer–Wallach measure for two, three, and four qubits. We determine the
four-qubit state, symmetric under exchange of qubit labels, which maximizes this
measure. It is also shown how the elementary monotones may be computed as a
function of observable quantities. We compute the magnitude of our measure for
the ground state of the four-qubit superconducting experimental system investi-
gated in [M. Grajcar et al., Phys. Rev. Lett. 96, 047006 (2006)], and thus con-
ﬁrm the presence of global entanglement in the ground state.
KEY WORDS: Meyer–Wallach measure; elementary monotones; entanglement
monotones; global entanglement; four-qubit state; qubit labels.
PAC S: 03.65.Ud; 03.67.Lx.
Entanglement is perhaps the fundamental property distinguishing quan-
tum from classical physics. It underpins the violation of classical locally
realistic descriptions of nature displayed by the Einstein–Podolsky–Rosen
Department of Physics, Haverford College, 370, Lancaster Avenue, Haverford, PA
D-Wave Systems Inc., 100-4401 Still Creek Drive, Burnaby, B.C., Canada V5C 6G9.
Department of Mathematics, Tufts University, Bromﬁeld–Pearson Building, Medford, MA
Frontier Research System, RIKEN, Wako-shi, Saitama, 351-0198, Japan.
Institute for Physical High Technology, P.O. Box 100239, D-07702 Jena, Germany.
Department of Solid State Physics, Comenius University, SK-84248, Bratislava, Slovakia.
Physics and Astronomy Dept., The University of British Columbia, 6224 Agricultural Rd.,
Vancouver, B.C., Canada V6T 1Z1.
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